TY - JOUR
T1 - Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order
AU - Kashkari, Bothayna S.H.
AU - Syam, Muhammed I.
N1 - Funding Information:
This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University , Jeddah, under Grant no. ( 363–47–D1436 ). The authors, therefore, gratefully acknowledgment the DSR technical and financial support.
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/11/1
Y1 - 2016/11/1
N2 - This paper is devoted to both theoretical and numerical study of Riccati equation with fractional order. A formulation to the fractional-order Legendre operational matrix of fractional integration is constructed. Existence and uniqueness results for the considered problem are provided and proved. The fractional derivative is described in the Caputo sense. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm.
AB - This paper is devoted to both theoretical and numerical study of Riccati equation with fractional order. A formulation to the fractional-order Legendre operational matrix of fractional integration is constructed. Existence and uniqueness results for the considered problem are provided and proved. The fractional derivative is described in the Caputo sense. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm.
KW - Fractional-order Legendre function
KW - Operational matrix of fractional integration
KW - Riccati equation with fractional order
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U2 - 10.1016/j.amc.2016.06.003
DO - 10.1016/j.amc.2016.06.003
M3 - Article
AN - SCOPUS:84975865138
SN - 0096-3003
VL - 290
SP - 281
EP - 291
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -